| Summary: | Recent decades have shown an explosion in the quantity and quality of geodetic data, mainly space-based geodetic data, that are being applied to geological and anthropogenic hazards. This has produced the need for new approaches for analyzing, modeling and interpreting these geodetic data. Typically, modeling of deformation and gravity changes follows an inverse approach using analytical or numerical solutions, where normally regular geometries (point sources, disks, prolate or oblate spheroids, etc.) are assumed at the initial stages and the inversion is carried out in a linear context. Here we review an original methodology for the simultaneous, nonlinear inversion of gravity changes and/or surface deformation (measured with different techniques) to determine 3D (three-dimensional) bodies, without any a priori assumption about their geometries, embedded into an elastic or poroelastic medium. Such a fully nonlinear inversion has led to interesting results in volcanic environments and in the study of water tables variation due to its exploitation. This methodology can be used to invert geodetic remote sensing data or terrestrial data alone, or in combination.
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